I PF Integral Bee: Share Interesting/Quirky Integrals!

  • I
  • Thread starter Thread starter ergospherical
  • Start date Start date
  • Tags Tags
    Integration
AI Thread Summary
The discussion invites participants to share interesting and quirky integrals, fostering a collaborative exploration of unique mathematical concepts. One integral shared is the definite integral from 0 to 1 of ln(x+1)/(x^2+1), which has sparked fascination due to its connection to the derivative of the natural logarithm. The thread emphasizes the enjoyment of discovering and understanding integrals, even for those who may not study them rigorously. Participants are encouraged to contribute their own intriguing integrals to enrich the conversation. Overall, the thread aims to create a fun and engaging environment for integral exploration.
ergospherical
Science Advisor
Homework Helper
Education Advisor
Insights Author
Messages
1,098
Reaction score
1,385
Thought it could be fun to have a sort of "PF Integral Bee"... if you know some interesting/quirky/etc. integrals then post them here! 🤓

To get the ball rolling...
1. ##\displaystyle{\int_0^1} \dfrac{\ln{(x+1)}}{x^2+1} dx##
 
Reply
  • Like
  • Love
Likes Greg Bernhardt, mcastillo356, Hamiltonian and 1 other person
Mathematics news on Phys.org
Not studied integrals seriously, but for me it has been really fascinating to understand ##\dfrac{d}{dx}\ln x=\dfrac{1}{x}##. The demonstration is similar to the demonstration of fundamental theorem of calculus.
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »
Thread 'Video on imaginary numbers and some queries'

Thread 'Video on imaginary numbers and some queries'

Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
View full post »
Thread 'Unit Circle Double Angle Derivations'

Thread 'Unit Circle Double Angle Derivations'

Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
View full post »

Similar threads

I Using recurrence formula to solve Legendre polynomial integral
Replies
3
Views
2K
I Error propagation of a variable for an integral
Replies
6
Views
4K
I How Can We Simplify Evaluating the Improper Integral of Logarithmic Functions?
Replies
10
Views
2K
A Help needed with derivation: solving a complex double integral
Replies
1
Views
2K
Solve the given problem involving integration
Replies
6
Views
2K
B Integral of cosecant function: understanding different approaches
Replies
14
Views
3K
MHB Integral using integration by parts
Replies
4
Views
2K
I Why does the integral of sine of x^2 from - infinity to + infinity diverge?
Replies
4
Views
2K
B Integration by Parts, an introduction I get confused with
Replies
2
Views
2K
I Substitution in a definite integral
Replies
6
Views
3K

Hot Threads

Recent Insights

Back
Top